Alicia runs 8 miles in 6 days. By setting up a proportion, it's calculated that it will take her 27 days to run 36 miles at the same rate.
Calculating Days Needed to Run a Total Distance:
Alicia runs 8 miles in 6 days. To find out how many days it will take her to run 36 miles, we can set up a proportion. Since the number of days is directly proportional to the miles run, we can use the equation:
8 miles / 6 days = 36 miles / x days
By cross-multiplying, we get:
8 miles * x days = 6 days * 36 miles
x = (6 days * 36 miles) / 8 miles
The miles cancel out, leaving us with:
x = 216 / 8
x = 27 days
Therefore, it will take Alicia 27 days to run a total of 36 miles if she continues running at the same rate.
£2300 is invested for 4 years at 5% per year simple interest.
Work out the total interest.
Answer:
The total interest is £460.
Step-by-step explanation:
Formula
[tex]Simple\ interest = \frac{Principle\times Rate\times Time}{100}[/tex]
As given
£2300 is invested for 4 years at 5% per year simple interest.
Principle = £2300
Rate = 5%
Time = 4 years
Put in the formula
[tex]Simple\ interest = \frac{2300\times 5\times 4}{100}[/tex]
[tex]Simple\ interest = \frac{46000}{100}[/tex]
Simple interest = £460
Therefore the total interest is £460.
Answer: £460
Step-by-step explanation:
Use this formula to find the total interest [tex]I=\frac{P*R*T}{100}[/tex]
I stands for interest, P is principal, R is rate, and T is time.
Principle = £2300
Rate = 5%
Time = 4 years
[tex]\frac{2,300*5*4}{100} =\frac{46,000}{100} =460[/tex]
Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! :-)
- Cutiepatutie ☺❀❤
Find the tenth term in each sequence. -1,2/3,7/3,4,17/3
It'a an arithmetic sequence:
[tex]a_1=-1\\\\a_2=-1+\dfrac{5}{3}=-\dfrac{3}{3}+\dfrac{5}{3}=\dfrac{2}{3}\\\\a_3=\dfrac{2}{3}+\dfrac{5}{3}=\dfrac{7}{3}\\\\a_4=\dfrac{7}{3}+\dfrac{5}{3}=\dfrac{12}{3}=4\\\\a_5=4+\dfrac{5}{3}=\dfrac{12}{3}+\dfrac{5}{3}=\dfrac{17}{3}\\\vdots\\\\\text{The general formula for nth term of an arithmetic sequence}\\\\a_n=a_1+(n-1)d\\\\\text{We have}\ a_1=-1\ \text{and}\ d=\dfrac{5}{3}.\\\\\text{Substitute}\\\\a_n=-1+(n-1)\left(\dfrac{5}{3}\right)=-1+\dfrac{5}{3}n-\dfrac{5}{3}=\dfrac{5}{3}n-\dfrac{3}{3}-\dfrac{5}{3}[/tex]
[tex]\boxed{a_n=\dfrac{5}{3}n-\dfrac{8}{3}}[/tex]
Final answer:
The sequence increases by 5/3 with each term. Using the formula T(n) = T(1) + (n-1)d, where T(1) is the first term, n is the term number, and d is the common difference, the tenth term of the sequence is determined to be 14.
Explanation:
The sequence provided is -1, 2/3, 7/3, 4, 17/3. To find the pattern, let's examine the differences between the terms:
2/3 - (-1) = 5/3
7/3 - 2/3 = 5/3
4 - 7/3 = 5/3
17/3 - 4 = 5/3
It appears that this sequence increases by 5/3 with each term. To find the tenth term, we start by finding the number of steps to get from the first term to the tenth term, which is 9 steps (since we are already given the first term).
To calculate the tenth term, we use the formula for the nth term of a sequence with a common difference: T(n) = T(1) + (n-1)d, where T(1) is the first term, n is the term number, and d is the common difference.
T(10) = -1 + (10-1)(5/3) = -1 + 45/3 = 14
Therefore, the tenth term of the sequence is 14.
Help me!!! Give me steps how to make this look like I showed my work on paper.
Answer:
p=2
Step-by-step explanation:
3(p+1)=9
3 x ? = 9
3x3=9
p+1 = 3
P=2
3(2+1)=9
3(3)=9
9=9
BRAINLIEST?
Answer:
Step-by-step explanation:
divide by three on both sides of the equal sign.
Then subtract one from from both sides of the equal sign.
the answer is p=2
3(p+1)=9
(p+1)=3
p=2
Find the number if 5.5% of it is 17% of 11
Answer:
The number is 34.
Step-by-step explanation:
Let the number be x.
As per the statement: if 5.5% of it is 17% of 11.
⇒ 5.5% of x is 17% of 11.
"5.5%of x" means [tex]\frac{5.5}{100} \times x[/tex]
"17% of 11" means [tex]\frac{17}{100} \times 11[/tex]
then;
[tex]\frac{5.5x}{100} = \frac{17 \times 11}{100}[/tex]
Multiply by 100 on both sides, we get;
[tex]\frac{5.5x}{100} \times 100 = \frac{17 \times 11}{100} \times 100[/tex]
Simplify:
[tex]5.5x = 187[/tex]
Divide both sides by 5.5 , we get;
[tex]\frac{5.5x}{5.5} = \frac{187}{5.5}[/tex]
Simplify:
x = 34
Therefore, the number is 34.
Answer:
Step-by-step explanation:
First we must find 17% of 11.
0.17 x 11 = 1.87
So we know 5.5% of "a number" or "x" is equal to 1.87
0.055x = 1.87
x = 1.87/0.055
x = 34
14. 30/r
r = 5
Need help!?
Answer:
The expression = 6
Step-by-step explanation:
The expression is 30/r
30/r
Substitute r=5
30/5
6
A lotion is made from an oil blend costing $1.50 per ounce and glycerin costing $1.00 per ounce. Four ounces of lotion costs $5.50.

Which value could replace x on the table?
(4 – g) 1.5
(4 – g) + 1.5
4g – g(1.5)
(4 – g)g
Plz provide a 'Table'
Answer:
the answer is A.(4-g)1.5
Step-by-step explanation:
Please help. Will reward brainliest
Answer: B
Step-by-step explanation:
if 90 is 80 percent of the value what is the value
Isabel is mailing packages. Each small package costs her $2.30 to send. Each large package costs her $3.60 . How much will it cost her to send 5 small packages and 4 large packages? (im not very smart)
Answer:
the answer is 25.9 round it to 26 if needed
Step-by-step explanation:
2.30 * 5 =11.50
3.60 * 4 =14.4
11.50+14.4=25.9
Well first let's do the small packages $2.30 * how many your sending which is 5. $2.30 * 5 = $11.50 and do the same for the big packages 3.60 * 4 = $14.40. Now add up both $11.50 + $14.40 = 25.90
Hope That Helps
If the length of a rectangle is 7/8 and the width is 1/4 of a meter then what is the area, A=lw, of the rectangle
Answer:
7/32 square meters
Step-by-step explanation:
Multiply the fractions. The numerators multiply to 7*1 = 7. The denominators multiply to 4*8 = 32. This is why (7/8)*(1/4) = 7/32. The units are "square meters" to indicate we're dealing with area instead of a linear measurement.
note: 7/32 = 0.21875
Answer:
7/32 square meters
Step-by-step explanation:
The area of a rectangle is A = L * W.
Here, that area is A = (7/8)(meter)(1/4)(meter) = 7/32 meter^2.
Jacob mixes 1/3 cup o yellow paint for every 1/5 cup of blue paint to make green paint how many cups of yellow paint are needed for one cup of blue paint
Answer:
[tex]\dfrac{5}{3}[/tex] cups
Step-by-step explanation:
Jacob mixes [tex]\dfrac{1}{3}[/tex] cup of yellow paint for every [tex]\dfrac{1}{5}[/tex] cup of blue paint to make green paint.
The ratio of yellow paint to blue paint = [tex]\dfrac{1}{3}:\dfrac{1}{5}[/tex]
= 5:3
[tex]\dfrac{1}{5}[/tex] cup of blue paint = [tex]\dfrac{1}{3}[/tex] cup of yellow paint
1 cup of blue paint = [tex]\dfrac{1}{3}\div\dfrac{1}{5}[/tex] cup of yellow paint
[tex]\Rightarrow \dfrac{1}{3}\div\dfrac{1}{5}[/tex]
[tex]\Rightarrow \dfrac{5}{3}[/tex]
Hence, For 1 cup of blue paint needed [tex]\dfrac{5}{3}[/tex] cups of yellow paint.
5Y+2-3(4Y)=0
WHAT DOES THIS EQUAL
Hello.
Y= 2/7
Step 1: Simplify both sides of the equation.
5y+2−3(4y)=0
5y+2+−12y=0
(5y+−12y)+(2)=0(Combine Like Terms)
−7y+2=0
Step 2: Subtract 2 from both sides.
−7y+2−2=0−2
−7y=−2
Step 3: Divide both sides by -7.
−7y/−7=−2/−7
y=2/7
Have a nice day.
Aidens age Is 1/7 of his father’s age. His father will be 61 years old in five years. In how many years will Aidens age be 1/5 of his fathers age ?
Answer:
see below PLEASE GIVE BRAINLIEST
Step-by-step explanation:
Aiden's father will be 61 in 5 years:
61 - 5 = 56
Since Aiden is 1/7 of his father's age just divide his father's age by 7:
56 ÷ 7 = 8 Aiden is currently 8 years old.
Aiden his father is he 1/5 his fathers age
9 57 9 x 5 = 45 NO
10 58 10 x 5 = 50 NO
11 59 11 x 5 = 55 NO
12 60 12 x 5 = 60 YES
Aiden is 1/7 of his father's current age, and his father is currently 56. Given that we want Aiden's age to be 1/5 of his father's, the number of years that would need to pass is 14 years.
Explanation:Firstly, let's determine Aiden's current age and his father’s current age. We know that Aiden's age is 1/7 of his father’s age, and that his father will be 61 in five years, meaning that his father is currently 56. Thus, Aiden, being 1/7 of his father’s age, is 8 years old.
Let's denote the number of years that we are looking for as 'x'. In 'x' years, Aiden will be 8+x years old, and his father will be 56+x. For Aiden’s age to be 1/5 of his father’s age, the following must be true: (8+x) = 1/5*(56+x). Solving this equation gives us x = 14. Therefore, in 14 years, Aiden's age will be 1/5 of his father's age.
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.Select the correct answer from the drop-down menu. Find the polynomial. {5} is the solution set of
x^2-5x+25=0
x^2+10x+25=0
x^2-10x+25=0
x^2+5x+25=0
Answer:
x^2-10x+25=0
Step-by-step explanation:
Cost: 10.00
Markup Rate 60%
What is the selling price and why?
(Help I don’t understand)
Answer:
$16
Step-by-step explanation:
$10 is the original price when it is out of the factory. If they are marking it up, they are raising the price by 60%. 160% of 10 is 16, so your answer is $16. Please mark my answer as brainliest
Ben thinks that the slope ratio for this triangle is 7/10. Carlissa thinks the ratio is 10/7 Who is correct? Explain your thinking fully.
Answer:
Both answers are correct, depending on the angle taken as reference
Step-by-step explanation:
we know that
In a right triangle
The slope ratio of the triangle is equal to the function tangent
The function tangent in a right triangle is equal to the opposite side to the angle divided by the adjacent side to the angle
so
[tex]tan(35)=\frac{7}{10}[/tex] -----> Ben's ratio
and
[tex]tan(55)=\frac{10}{7}[/tex] ------> Carlissa's ratio
therefore
The slope will depend on the angle taken as a reference
so
Both answers are correct, depending on the angle taken as reference.
Mora is using a map to find the distance between her house and her cousin's house. She knows that $2$ centimeters on the map represent $300$ miles. On the map, the distance between her house and her cousin's house is $20$ centimeters.
Answer:
Step-by-step explanation:
2÷20= 10 × 300= 3,000 miles
The distance between her house and her cousin's house is 3000 miles.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 hour = 60 seconds
1 minute = 60 seconds
1 km = 1000 m
We have,
2 cm = 300 miles
The distance between her house and her cousin's house.
= 20 cm
= 10 x 2 cm
= 10 x 300
= 3000 miles
Thus,
3000 miles is the distance between her and her cousin's house.
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if lines m and n are parallel, and < 8 measures 110°, which is the measure of < 7?
a. 40°
b. 70°
c. 90°
d. 110°
The ordered pairs model an exponential growth function.
{(−1,21.875), (0,35), (1,56), (2,89.6)}
What is the function equation?
Enter your answer in the box.
Answer:
[tex]y=35\cdot (1.6)^x.[/tex]
Step-by-step explanation:
Find the exponential function in a form [tex]y=a\cdot b^x.[/tex]
1. At x=0,
[tex]35=a\cdot b^0=a.[/tex]
2. At x=1,
[tex]56=35\cdot b^1\Rightarrow b=\dfrac{56}{35}=\dfrac{8}{5}=1.6.[/tex]
Therefore, the expression for the exponential function is
[tex]y=35\cdot (1.6)^x.[/tex]
Note that
[tex]y(-1)=35\cdot (1.6)^{-1}=\dfrac{35}{1.6}=21.875[/tex]
and
[tex]y(2)=35\cdot (1.6)^2=35\cdot 2.56=89.6.[/tex]
The exponential growth function represented by the provided set of ordered pairs is[tex]y = 35 \times 1.6^x,[/tex] where 'a' is the initial value and 'b' is the growth factor derived from the given points.
Explanation:To begin determining the underline equation of this exponential growth function, we first need to recognize that the general form of an exponential function is[tex]y = ab^x[/tex] , where a is the initial value (the output when x=0) and b is the growth factor.
In the provided set of ordered pairs, when x = 0, y = 35. Therefore, a = 35. Now, to calculate b, we could apply the function to the point (1,56). We know that[tex]56 = 35\times b^1,[/tex]which simplifies to 56 = 35b. Solving for b gives us b ≈ 1.6 (approximation).
So, the exponential growth function that corresponds to these ordered pairs is[tex]y = 35\times 1.6^x.[/tex]
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describe the ored of operations in this expression find the number it equals.
[tex] \sqrt{64 + (42 \div 6)} [/tex]
Answer:
√71
Step-by-step explanation:
Simplify 42÷6 to 7
√64+7
Simplify 64+7 to 71
=√71
Which expressions are equivalent to this expression?
3(n+4)
Select each correct answer.
2n+12+n
12+n+n+n
3n−12
3n−12
Answer:
12+n+n+n
Step-by-step explanation:
3(n+4)
Distribute 3.
3 x n = n+n+n
3 x 4 = 12
12+n+n+n
Mary is twice as old as Jane was when Mary was as old as Jane is now. The sum of their ages is 28. What is the age of each girl?
Answer:
Mary's age is 16.8 years
Jane's age is 11.2 years
Step-by-step explanation:
Let's assume Jane was x years old
Mary is twice as old as Jane a long time ago
so, Marry's age =2x
difference in age =2x-x=x years
It means that Marry is x year older than Jane
now, we have
Mary was as old as Jane is now
or we can say that
Jane is as old as Mary was
we know that
Mary =2x years
so, Jane age becomes
Jane=2x years
and we have got
As Mary is x years older than Jane
so, Mary's age =2x+x=3x years old now
now, we are given
The sum of their ages is 28
So,
Mary's age + Jane's age =28
[tex]3x+2x=28[/tex]
[tex]5x=28[/tex]
[tex]x=5.6[/tex]
Mary's age is
[tex]=3\times 5.6[/tex]
[tex]=16.8[/tex]
Jane's age is
[tex]=2\times 5.6[/tex]
[tex]=11.2[/tex]
a cone has a radius of 6cm and height 9 calculate a)the volume and curved surface area b) total surface area
Answer:
V = 339.3 cm³; L = 203.9 cm²; A = 317.0 cm²
Step-by-step explanation:
a) Volume
The formula for the volume (V) of a cone is
V = ⅓πr²h
V = ⅓π × 6² × 9
V = ⅓π × 36 × 9
V = 108π cm³
V ≈ 339.3 cm³
=====
Curved surface area
The formula for the lateral surface area (L) of a cone is
L = πr√(r² + h²)
L = π×6√(36 + 81)
L = 6π√[9(4 + 9)]
L = 6π√(9 × 13)
L = 18π√13 cm²
L ≈ 203.9 cm²
===============
b) Base surface area
The base is a circle, so the formula for base surface area (B) is
B = πr²
B = π×6²
B = 36π cm²
B ≈ 113.1 cm²
=====
Total surface area
A = L + B
A = 18π√(13 +36π)
A = 18π(2 + √13) cm²
A ≈ 203.9 + 113.1
A ≈ 317.0 cm²
what inequality represents the sentence the quotient of a number and 3 is no more than 15
Answer:
n/3 ≤ 15
Step-by-step explanation:
Quotient = n/3
The quotient cannot be greater than 15, but it can equal 15.
n/3 ≤ 15
The quotient of a number and 3 is no more than 15 represented by x/3 ≤ 15.
What is problem-solving?
Problem-solving is defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. For example, a trainer may need to figure out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
Solution:
let the number be X
x/3 ≤ 15
Quotient = x/3
Since the quotient cannot be greater than 15, it can equal 15.
∴ x/3 ≤ 15
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You went to lunch with your friend and the bill was $19 your lunch is three dollars more than your friends how much was your friends lunch
Answer:
Let x = cost of your friend's lunch.
x + x + 3 = 19
x= 8
Answer:
Your friend lunch bill is $8
Step-by-step explanation:
The bill for you and your friend lunch = $19
Meaning the sum of your lunch bill and your friend bill is $19.
To find how much your friend bill is,
Let represent your friend bill to be x and your bill to be y.
Therefore: x + y = $19
Given that your bill is $3 more than your friend.
Simple means; your bill = your friend bill + 3
Since x represent your friend bill and y represent your bill
So
y = x + 3
Therefore from: x + y = $19
Substitute the value of y = x+3
x + y = $19
x + x + $3= $19
2x = $19 - $3
2x = 16
x = 16/2
x = $8
Since x = your friend bill.
Therefore:.
Your friend lunch bill is $8
If f(x) = –2x + 7 and g(x) = x2 – 2, what is [f o g](3)?
–7
–1
1
7
[tex]f(x)=-2x+7\\\\g(x)=x^2-2\\\\\ [f\ \circ\ g](x)=-2(x^2-2)+7=-2x^2+4+7=-2x^2+11\\\\\text{Put x = 3 to the equation of the function}\\\\\ [f\ \circ\ g](3)=-2(3^2)+11=-2(9)+11=-18+11=-7\\\\Answer:\ \boxed{-7}[/tex]
Answer:
The value of [f o g](3) is -7
Step-by-step explanation:
Given two functions
[tex]f(x)=-2x+7, g(x)=x^2-2[/tex]
we have to find [f o g](3)
[tex]f(x)=-2x+7[/tex]
[tex][f o g](x)=f(g(x))=f(x^2-2)=-2(x^2-2)+7[/tex]
[tex][f o g](x)=-2x^2+4+7=-2x^2+11[/tex]
Put x=3
[tex][f o g](3)=-2(3)^2+11=-7[/tex]
The value of [f o g](3) is -7
Option 1 is correct
[tex]3(2x - 3) = 4(x + 1)[/tex]
solve the problem and show your work
Answer:
x = [tex]\frac{13}{2}[/tex]
Step-by-step explanation:
distribute parenthesis on both sides of the equation
6x - 9 = 4x + 4 ( subtract 4x from both sides )
2x - 9 = 4 ( add 9 to both sides )
2x = 13 ( divide both sides by 2 )
x = [tex]\frac{13}{2}[/tex]
a flat surface made up of points that extends indefinitely in all directions
Good morning Sir/Ma'am!
Answer:
A plane is a flat surface made up of points that extends infinitely in all directions.
Hope this helps! Have a great day!
~Sky
Which equation represents a proportional situation? y = 6x + 4 y = –3x + 10 y = –2x – 14 y = 14x
The equation of proportional situation is y = ax.
Therefore your answer is y = 14x
HI CAN SOMEONE PLZ HELP ME I HAVE NO CLUE HOW TO DO THIS SOS. THANKS SM!!!❤️❤️❤️
Problem 1)
This question is incomplete. It asks us to find something, but doesn't say what to find. It's literally blank after the word "find" which suggests your teacher made a typo. Please get back to me on this. Thanks.
===================================
Problem 2)
Angles GAR and GAT are supplementary because they are a linear pair. They form a straight angle. So we add up the expressions of x for each of these angles, solve for x, and use this to find angle GAR.
(angle GAR) + (angle GAT) = 180
(5x) + (3x+4) = 180
8x+4 = 180
8x+4-4 = 180-4
8x = 176
8x/8 = 176/8
x = 22
Note: now that I reached this point I realize that this might be the answer to problem 1; however, I'm not 100% sure because of the incomplete problem.
Use this x value to find angle GAR
angle GAR = 5*x
angle GAR = 5*22
angle GAR = 110
Unfortunately this answer isn't listed. I'm thinking your teacher made another typo.
===================================
Problem 3)
Answer: angle GAR and angle ABQ are corresponding angles.
Thankfully this answer is listed. Corresponding angles are angles that are on the same side of the transversal line and they are either both above or below the parallel lines they are next to. In this case, they are both above the parallel line counerparts.
===================================
Problem 4)
Corresponding angles are congruent as long as we have a set of parallel lines. So that means angle ABQ is equal to angle GAR. So angle ABQ is also 110 degrees
===================================
Problem 5)
angle BAT = angle GAR, because they are vertical angles
angle BAT = 110
angle BAT = (angle BAD) + (angle DAT)
(angle BAD) + (angle DAT) = angle BAT
(100) + (angle DAT) = 110
angle DAT = 110-100
angle DAT = 10
angle ADB = angle DAT, because they are alternate interior angles
angle ADB = 10
--------
Final Answer: 10 degrees